Description of nuclear systems with a self-consistent configuration-mixing approach. I: Theory, algorithm, and application to the ${}^{12}$C test nucleus

Abstract

Although self-consistent multi-configuration methods have been used for decades to address the description of atomic and molecular many-body systems, only a few trials have been made in the context of nuclear structure. This work aims at the development of such an approach to describe in a unified way various types of correlations in nuclei, in a self-consistent manner where the mean-field is improved as correlations are introduced. The goal is to reconcile the usually set apart Shell-Model and Self-Consistent Mean-Field methods. This approach is referred as "variational multiparticle-multihole configuration mixing method". It is based on a double variational principle which yields a set of two coupled equations that determine at the same time the expansion coefficients of the many-body wave function and the single particle states. The formalism is derived and discussed in a general context, starting from a three-body Hamiltonian. Links to existing many-body techniques such as the formalism of Green's functions are established. First applications are done using the two-body D1S Gogny effective force. The numerical procedure is tested on the ${}^{12}$C nucleus in order to study the convergence features of the algorithm in different contexts. Ground state properties as well as single-particle quantities are analyzed, and the description of the first $2^{+}$ state is examined. This study allows to validate our numerical algorithm and leads to encouraging results. In order to test the method further, we will realize in the second article of this series, a systematic description of more nuclei and observables obtained by applying the newly-developed numerical procedure with the same Gogny force. As raised in the present work, applications of the variational multiparticle-multihole configuration mixing method will however ultimately require the use of an extended and more constrained Gogny force.

22 pages, 18 figures, accepted for publication in Phys. Rev. C. v2: minor corrections and references added

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Cited by in corpus (14)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Entanglement Rearrangement in Self-Consistent Nuclear Structure Calculations
• Ab initio no-core solutions for ${}^6$Li
• The time-dependent generator coordinate method in nuclear physics
• Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model
• Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories
• Description of nuclear systems with a self-consistent configuration-mixing approach. II: Application to structure and reactions in even-even sd-shell nuclei
• An extension of the generator coordinate method with basis optimization
• Gogny-force derived effective shell-model Hamiltonian
• Reduction in nuclear size and quadrupole deformation of high-spin isomers of 127,129In
• Impact of finite-range spin-orbit and tensor terms in Gogny EDF
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Deformed natural orbitals for ab initio calculations